Most computer speakers like that typically have the amp built into the sub. Why do you want to build your own amp, it's be significantly easier and less expensive to buy an amp.
I had a RadioShack speaker that was rated for 40 Whats. I used it at the beach for many years. Then I connected it to my home stereo and fed it 70 Watts RMS for years. Its woofer finally burned out, it was stamped- "5W nominal- Korea".